Defect indices of singular symmetric linear difference equations with complex coefficients

Abstract

This article is concerned with the defect indices of singular symmetric linear difference equations of order 2n with complex coefficients and one singular endpoint. We first show that the positive and negative defect indices d + and d -of a class of singular symmetric linear difference equations of order 2n with complex coefficients satisfy the inequalities n ≤ d + = d -≤ 2n and all values of this range are realized. This extends the result for difference equations with real coefficients. In addition, some sufficient conditions for the limit point and the strong limit point cases are given.